Question

180°

1. 30° + 50° + m∠k = 180° 3. substitution property
2. 80° + m∠k = 180° 4. addition
3. m∠k = 100° 5. subtraction property of equality
4. m∠j = m∠p; m∠k = m∠n 6. substitution
5. ∠j ≅ ∠p; ∠k ≅ ∠n 7. if angles are equal then they are congruent
6. △hkj ~ △lnp 8. aa similarity theorem

which reason is missing in step 2?
○ cpctc
○ definition of supplementary angles
○ triangle parts relationship theorem
○ triangle angle sum theorem

Explanation:

To determine the missing reason in step 2, we analyze the context. Step 3 involves the sum of angles in a triangle (\(30^\circ + 50^\circ + m\angle K = 180^\circ\)), which relates to the triangle angle sum theorem (the sum of interior angles of a triangle is \(180^\circ\)). Other options: CPCTC is for congruent triangles' corresponding parts, supplementary angles are for \(180^\circ\) linear pairs, and "triangle parts relationship theorem" is not a standard term here. The triangle angle sum theorem explains the sum of angles in a triangle being \(180^\circ\), matching step 2's context (leading to step 3's equation).

Answer:

triangle angle sum theorem